Quantifying the interplay between gravity and magnetic field in molecular clouds - a possible multi-scale energy equipartition in NGC6334

TL;DR

This paper investigates the multi-scale energy balance between gravity and magnetic fields in molecular clouds, proposing a formalism to compare their spectra and applying it to NGC6334, revealing near equipartition at various scales.

Contribution

It introduces a new formalism to quantify the multi-scale distribution of magnetic and gravitational energies in molecular clouds, linking magnetic field-density relations with surface density PDFs.

Findings

Magnetic and gravitational energies are in near equipartition in NGC6334 across multiple scales.

The formalism connects magnetic energy spectrum with surface density PDF and magnetic field-density relation.

Current observations are limited; more multi-scale measurements are needed for broader validation.

Abstract

The interplay between gravity, turbulence and the magnetic field determines the evolution of the molecular ISM and the formation of the stars. In spite of growing interests, there remains a lack of understanding of the importance of magnetic field over multiple scales. We derive the magnetic energy spectrum -- a measure that constraints the multi-scale distribution of the magnetic energy, and compare it with the gravitational energy spectrum derived in Li \& Burkert (2016). In our formalism, the gravitational energy spectrum is purely determined by the surface density PDF, and the magnetic energy spectrum is determined by both the surface density PDF and the magnetic-field-density relation. If regions have density PDFs close to $P(\Sigma)\sim \Sigma^{-2}$ and a universal magnetic field-density relation $B\sim \rho^{1/2}$, we expect a multi-scale near equipartition between gravity and the magnetic fields. This equipartition is found to be true in NGC6334 where estimates of magnetic fields over multiple scales (from 0.1 pc to a few parsec) are available. However, the current observations are still limited in sample size. In the future, it is necessary to obtain multi-scale measurements of magnetic fields from different clouds with different surface density PDFs and apply our formalism to further study the gravity-magnetic field interplay.